Spacings around and order statistic

Nagaraja, H. N.; Bharath, Karthik; Zhang, Fangyuan

Abstract

We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic Xk:n of a random sample of size n from a continuous distribution F. For central and intermediate cases, normalized spacings in the left and right neighborhoods are asymptotically i.i.d. exponential random variables. The associated independent Poisson arrival processes are independent of Xk:n. For an extreme Xk:n, the asymptotic independence property of spacings fails for F in the domain of attraction of Fréchet and Weibull (α≠1) distributions. This work also provides additional insight into the limiting distribution for the number of observations around Xk:n for all three cases.

Citation

Nagaraja, H. N., Bharath, K., & Zhang, F. (2015). Spacings around and order statistic. Annals of the Institute of Statistical Mathematics, 67(3), https://doi.org/10.1007/s10463-014-0466-9

• Journal Article Type: Article
• Acceptance Date: Apr 26, 2014
• Online Publication Date: Apr 26, 2014
• Publication Date: Jun 30, 2015
• Deposit Date: Jun 19, 2017
• Publicly Available Date: Jun 19, 2017
• Journal: Annals of the Institute of Statistical Mathematics
• Print ISSN: 0020-3157
• Electronic ISSN: 1572-9052
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 67
• Issue: 3
• DOI: https://doi.org/10.1007/s10463-014-0466-9
• Keywords: Spacings; uniform distribution; central order statistics; intermediate order statistics; extremes; Poisson process.
• Public URL: https://nottingham-repository.worktribe.com/output/753476
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10463-014-0466-9
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10463-014-0466-9.